Make another object invisible from Boolean for OBJ ewport
You haven't selected Selection only when you export .obj-file.
Select your object. Select File -&gt; Export -&gt; Wavefront (.obj).
Check Selection Only checkbox and press Export OBJ

To fix the topology you need to make sure that there are no overlapping edges.
You can see your object wireframe by checking Wireframe checkbox under Object Properties panel from Viewport Display. You should check this to your object (The Cube).
From same panel change Display As to Bounds for your cutter (The Sphere). This way you can see if there are overlapping edges. Raise or lover the sphere so the edges are as far from each other as possible.


And also .obj export is not very good with quads so you need to make all your faces into triangles. Select your object and in Edit Mode press A to select all. Select Face and Triangulate Faces.